Watch out, ExxonMobil (NYSE:XOM): Royal Dutch Shell (NYSE:RDS-A) (NYSE:RDS-B) is breathing down your neck for recognition as the majordomo of Big Oil.

In the June-ended quarter, Shell, the biggest of the European integrated companies, earned $11.56 billion, only slightly less than Exxon's $11.68 billion. That, for Shell, represented a 33% year-over-year increase.

Of course, Shell isn't riding solo here. As with other Big Oil companies, including Exxon, ConocoPhillips (NYSE:COP), and BP (NYSE:BP), it predictably benefited from huge increases in global crude prices during the past year, while watching the related gains offset somewhat by slim refinery margins, especially in North America. In the U.S., the company's realized crude oil price reached more than $118 a barrel for the quarter. As a result, Shell's upstream operations yielded 90% more income than a year ago.

According to CEO Jeroen van der Veer, Shell expects to deploy $35 billion to $36 billion in capital spending this year, up materially from the previous expectation of $24 billion to $25 billion. The new range includes $5.8 billion for Duvernay Oil, which, among other locations, is active in the Montney tight sands gas play in western Canada. But Shell has found the going tough in some international venues. For instance, earlier this week it indicated that it won't be able to meet export expectations from Nigeria, following a rash of tribal violence there.

My approach to Shell -- which could be undervalued relative to the group -- will be to watch it carefully, especially because I'm intrigued by its willingness to put its money where its exploratory mouth is. But for now, I'd rather cast my cash toward the likes of U.S. independents like Chesapeake Energy (NYSE:CHK).

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Fool contributor David Lee Smith doesn't own shares in any of the companies mentioned above. He does welcome your comments. The Motley Fool has a globally recognized disclosure policy.